A perfect shuffle network of 2.times.2 nodes is a cost-effective interconnection network, for example, in large-scale parallel and distributed supercomputer systems, because it provides network connectivity from any of N network inlets to any of N network outlets in only log.sub.2 N stages. The inter-stage interconnection pattern assigns links consecutively to nodes in the next stage in a manner analogous to shuffling a deck of playing cards. There are a number of other known networks, such as the banyan and the crossover, which are topologically equivalent to the perfect shuffle although they each have their own specific interconnection pattern. For each of these networks, the number of inter-stage links between any pair of successive stages is equal to N, the number of network inlets. Photonic implementations of such networks using free-space optical interconnects are disclosed in U.S. patent application Ser. No. 296,284 of K. Brenner et al., filed Jan. 11, 1989, "Optical Shuffle Arrangement" and U.S. patent application Ser. No. 219,623 of J. Jahns et al., filed July 15, 1988, "Optical Crossover Network", both applications being assigned to the same assignee as the present invention. Networks of this type are, however, not fault-tolerant and have high blocking. The problem with the topology is that in a network having log.sub.2 N stages, there is only one path from a given network inlet to a given network outlet. Thus, if there is a fault on that path or some part of the path is busy, no communication is possible. An article of G. B. Adams et al., "The Extra Stage Cube: A Fault-Tolerant Interconnection Network for Supersystems", IEEE Transactions on Computers, Vol. C-31, No. 5, May 1982, discloses the addition of an extra stage to the network thus providing one additional path between any inlet and any outlet. Although this makes the network substantially more reliable, it still has an unacceptably high blocking probability. Furthermore, the simple addition of extra stages will never result in a point-to-point, strictly nonblocking network or even one with a blocking probability that is acceptably low in most high-traffic network applications.